What is the name of the fictional group of men who supposedly rule the world?

Are you refering to a global secret society called the Illuminati (the "Illuminated Ones" as they call themselves) have been holding the reigns of power in the world since ancient times, expanding their power out of the Middle and Near East (and other centres) to control first Europe and then, thanks to the British Empire and other European empires, to take over in the Americas, Africa, Australia, New Zealand, Asia, and elsewhere.

Because they aren't fictional, they're real.

OR perhaps you mean

A small number of extremely wealthy people, descendants of wealthy families in Europe and the U.S, own a major part of the material wealth of the world. This power is concentrated in London which is the centre of the world banking system. The control they exercise is kept within the original families and passed down from generation to generation. They are highly organised, operating in secret through a web of 'private' organisations.This group is known as the Global Elite, who are very real.

They work on the principle of "control of the money" (mints and banking systems) therby controlling the world. Use and read what's here on the link and you'll understand better.

Depends on who you ask but in general these: Illuminati Reptilians Skull and Bones Trilateral Commission Rothchilds Bilderbergers Zionists Nazis Mafia CIA NWO. As you can see the conspiracy buffs really don't have it together. Oh, and the real Illuminati broke up ca. 1785 and there has been no trace of them since. Which to a hoaxbuff, means "evidence that they are perfect at hiding", and to anyone else means "It's dead, Jim".